Geodesic
On coset-spaces of compact Lie groups by subgrops of corank two
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2017), pp. 68-77

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Let $G$ and $G'$ be compact connected simply connected Lie groups. Suppose that $G$ is a simple group, $L$ is a centralizer of torus of $G$, $H$ is the commutant of the subgroup $L$, and $\mathrm{rk}~G - \mathrm{rk}~H = 2$. Let $\mathrm{Sam}~(G/H) = 0$. We prove the following assertion: if the group $G'$ acts transitively and almost effectively on the manifold $G/H$, then $G' \cong G$. If all lenghts of roots of the group $G$ are equal, then the action of $G'$ on $G/H$ is similar to the action of $G$.
Mots-clés : compact Lie group
Keywords: cohomology, homotopy groups, transitive action. 
@article{IVM_2017_11_a7,
     author = {A. N. Shchetinin},
     title = {On coset-spaces of compact {Lie} groups by subgrops of corank two},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {68--77},
     publisher = {mathdoc},
     number = {11},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_11_a7/}
}
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A. N. Shchetinin. On coset-spaces of compact Lie groups by subgrops of corank two. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2017), pp. 68-77. http://geodesic.mathdoc.fr/item/IVM_2017_11_a7/